Back in December my sister flew DAY-JFK-MAD. DAY-JFK was with DL and JFK-MAD with IB. I'm pretty sure she mentioned both carries had an agreement and she was able to check her bags all the way to MAD. I don't think she had to pay any extra money either. The other 2 questions I cant answer. Have a good day!!

Is this in one ticket? I doubt as this is not really an alliance and DL would rather use UX for their onward travel, when it#s in one ticket. If it's in one ticket, then there is a interline agreement, and you will be fine.

So I am almost tempted to say, NO, it will not work. That said, since you have a status with DL, possibly you get a nice agent which will check the bags through when you show your second itinerary.

Also be aware that transferring from DL to IB in MAD is quite a hell. You will arrive at T1/2/3 and then pass immigration. You then pass the baggage claim area. If your bags are NOT checked through, you can catch them there (so it doesn't really make that a big difference if you check them through or not). Then you wait curbside for a free shuttle bus bringing you to T4, count approx 10-15 minutes ride for that, as both terminals are way apart. Then you go to the IB check in counters to get your boarding pass (do not even count on DL issuing you a onward boarding pass on IB even if you travel on one ticket). If you have bags, you can check them there again (if they're checked through make sure to show them your bag receipt so that they take care of transferring the bags). Then you proceed through security and board your next flight.

If bags are checked through, you will pass customs for your bags in PMI.

In any case, considering you need to go completely landside, it doesn't really make a difference if they check your bags through or not to be honest...

excellent that this worked. No, in this case you do not need to collect. It's a good thing in Schengen than other than i.e. in the US you do not need to collect them at first point of entry.

MAD is normally not bad when connecting. It is just your combination of airlines that is usually never booked and make it difficult, since you need to change terminals But if you have enough time, you will be fine. Make sure to mention your checked bags to IB and show them your bagage stubs when collecting your boarding pass at T4 for the IB flight.

Have fun in PMI. This island is full of tourists, but it's sooo beautiful. If you have a rental car and time, make a tour through the western Transmuntara mountain range, or go on the Formentor peninsula. Hope you are a good driver though